Question

describe the transformation
a. translation 2 units down
b. translation 6 units down
c. reflection across the y - axis
d. reflection across the x - axis

Explanation:

Step1: Analyze translation

Translation moves a figure without rotation or reflection. Counting vertical units between corresponding points of the two triangles: it's more than 2 units down (so A is wrong).

Step2: Analyze reflection

Reflection across y - axis would flip the figure horizontally (left - right). But here the orientation is same vertically. Reflection across x - axis flips the figure vertically (up - down). Counting vertical distance: if we take a point on the upper triangle (say top vertex) and its corresponding point on the lower triangle, the distance is 6 units down (which is a translation down 6 units as reflection across x - axis is a different transformation concept here. Wait, no - actually, checking each option:

• For translation: pick a vertex of the upper triangle (say \((- 3,5)\) - assuming grid where each square is 1 unit). The corresponding vertex of the lower triangle is \((-3,-1)\). The vertical change is \(y_2 - y_1=-1 - 5=-6\) (6 units down).
• Reflection across x - axis: formula \((x,y)\to(x, - y)\). If original point \((x,y)\), reflected over x - axis is \((x, - y)\). But if we assume a point \((-3,5)\), reflected over x - axis is \((-3, - 5)\) (not \((-3,-1)\)). Reflection across y - axis: \((x,y)\to(-x,y)\) (changes x - coordinate sign, not relevant here).

Answer:

B. translation 6 units down